Exam Body

Year

Subject

Paper Type

gce model questions vol1 2018 mathematics | Objective

Prepare for your exams with gce model questions vol1 questions? Reviewing past/model questions is one of the most effective ways to guarantee a high score. This practice hub features authentic 2018 mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

In a shop, the total cost of 3 pens and 2 notebooks is £12. Each pen costs £2 more than a notebook. Find the total cost of 7 pens and 4 notebooks.

A. 26.80

B. 28.40

C. 30.00

Correct D. 27.20

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 2 View Details

A positive integer \(n\) satisfies that the inequality \(n < x < 2n\) has exactly five integer solutions for \(x\), and the sum of those solutions is 45. Determine \(n\).

Correct A. 6

B. 5

C. 7

D. 8

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 3 View Details

The time \(T\) (in minutes) taken by a machine to process a batch varies directly with the number of operators \(n\) and inversely with the square of the speed setting \(s\). When 4 operators work at speed setting 3, the time is 12 minutes. Find the time required when 6 operators work at speed setting 2.

A. 45

B. 48

C. 36

Correct D. 40.5

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 4 View Details

In a circle, two chords \(AB\) and \(CD\) intersect at point \(E\) inside the circle. The lengths are \(AE = 3\) cm, \(EB = 5\) cm and \(CE = 4\) cm. The distance from the centre \(O\) of the circle to point \(E\) is 6 cm. Find (i) the length of \(ED\), and (ii) the radius of the circle.

A. ED = 3.0 cm; radius = sqrt(60) cm

B. ED = 5.0 cm; radius = sqrt(48) cm

C. ED = 4.2 cm; radius = sqrt(45) cm

Correct D. ED = 3.75 cm; radius = sqrt(51) cm

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 5 View Details

The Venn diagram shows three sets A, B and C. The numbers in the regions are: AB only = 20, AC only = 18, BC only = 24, and the region common to all three sets = 7. The universal set contains 120 elements, of which 20 are in none of the sets. It is also known that the number of elements that belong to exactly two of the sets is twice the number that belong to exactly one set, and that the numbers of elements belonging only to B and only to C are equal. Finally, set B contains 57 elements. Find the number of elements in set A.

Correct A. 64

B. 71

C. 82

D. 58

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 6 View Details

In the diagram, points P\((1,2)\), Q\((5,6)\) and R\((3,-1)\) are plotted. The line \(y = 2x - 1\) and the line \(x + y = 8\) intersect at a point I. A line L passes through I and is perpendicular to the line PQ. Find the distance from point R to line L. Give your answer in simplest surd form.

A. 3\sqrt{3}

B. 2\sqrt{2}

Correct C. 3\sqrt{2}

D. 4\sqrt{2}

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 7 View Details

Exam scores of 40 students are grouped as follows: \(40\le x\le49\):5, \(50\le x\le59\):9, \(60\le x\le69\):12, \(70\le x\le79\):8, \(80\le x\le89\):4, \(90\le x\le99\):2. Assume scores are uniformly distributed within each interval. (i) Estimate the mean score. (ii) Estimate the standard deviation. (iii) Estimate the percentage of students whose scores lie within one standard deviation of the mean. Give the final percentage to the nearest whole percent.

A. 55

B. 70

C. 58

Correct D. 63

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 8 View Details

The time \(T\) (in minutes) taken by a machine to process a batch varies directly as the number of items \(n\) and inversely as the square root of the power \(P\) (in kW) supplied to it. When 200 items are processed with a power of 25 kW, the time is 40 minutes. Find the power required to process 500 items in 30 minutes. Give your answer as an exact fraction.

A. 2250/9

B. 2750/9

C. 2500/8

Correct D. 2500/9

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 9 View Details

A line \(L\) passes through the point \(P(4,2)\) and is perpendicular to the line joining \(A(1,5)\) and \(B(7,-3)\). Find the area of the triangle formed by line \(L\) and the coordinate axes. Give your answer as a fraction in lowest terms.

A. 5/6

Correct B. 2/3

C. 4/3

D. 3/2

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 10 View Details

The system of equations \(\begin{cases}2x - y = k\\ 3x + 4y = 12\end{cases}\) has an integer solution for \(x\). Find the smallest positive integer value of \(k\) for which this occurs.

A. 12

Correct B. 8

C. 6

D. 10

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 11 View Details

Solve the inequality ( |2x-5| < x+3 ) and then find the sum of all integer values of (x) that satisfy it.

A. 26

B. 24

Correct C. 28

D. 30

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 12 View Details

The sum of the first four terms of an arithmetic progression is 50 and the sum of the first six terms is 84. Find the fifth term of the progression.

A. 67\/4

B. 63\/4

Correct C. 65/4

D. 13\/2

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 13 View Details

In a plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\), \(|\mathbf{b}| = 4\) and \(\mathbf{a}\cdot\mathbf{b} = 12\). Determine (i) the magnitude of \(\mathbf{a} - 2\mathbf{b}\) and (ii) the angle between \(\mathbf{a}\) and \(\mathbf{a} - 2\mathbf{b}\).

A. |\mathbf{a} - 2\mathbf{b}| = \sqrt{41}, \theta = \arccos\left(\frac{2}{5\sqrt{41}}\right)

Correct B. |\mathbf{a} - 2\mathbf{b}| = \sqrt{41}, \theta = \arccos\left(\frac{1}{5\sqrt{41}}\right)

C. |\mathbf{a} - 2\mathbf{b}| = \sqrt{45}, \theta = \arccos\left(\frac{2}{5\sqrt{41}}\right)

D. |\mathbf{a} - 2\mathbf{b}| = \sqrt{33}, \theta = \arccos\left(\frac{1}{4\sqrt{41}}\right)

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 14 View Details

A right circular cone has base radius \(3r\) and height \(4h\). A right circular cylinder of radius \(r\) is inscribed in the cone with its axis coincident with that of the cone. Find the ratio of the volume of the cylinder to the volume of the cone.

A. 4/9

Correct B. 2/9

C. 3/8

D. 1/3

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 15 View Details

In a school of 120 students, 10 study none of the subjects Mathematics, Physics and Chemistry. The number who study Mathematics is twice the number who study Physics, and the number who study Chemistry is 30 less than those who study Mathematics. Exactly 10 students study all three subjects. The number of students who study exactly one subject is three times the number who study exactly two subjects. How many students study exactly two of the three subjects?

A. 35

B. 20

C. 30

Correct D. 25

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 16 View Details

The decimal (0.\overline{36}\) is expressed as a fraction in lowest terms. Then find \(25\%\) of that fraction. Give your answer as a fraction in lowest terms.

Correct A. 1/11

B. 1/12

C. 3/22

D. 2/11

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 17 View Details

The sum of the first \(n\) terms of a sequence is given by \(S_n = n^{2} + 2n\). Find the 15th term of the sequence and also the sum of the terms from the 11th to the 20th inclusive.

A. 30, 315

B. 32, 330

C. 31, 300

Correct D. 31, 320

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 18 View Details

A box contains 5 white balls and an unknown number of black balls. Two balls are drawn successively without replacement. The probability that both drawn balls are black is \(\frac{3}{7}\). Determine the original number of black balls in the box.

A. 14

B. 8

Correct C. 10

D. 12

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 19 View Details

A shop marks up an item by \(40\%\) on its cost price and then offers a discount of \(20\%\) on the marked price. If the final selling price is £84, what was the original cost price of the item? Give your answer in pounds.

A. 80

B. 90

Correct C. 75

D. 70

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 20 View Details

If \(x + \frac{1}{x} = 3\), find the value of \(x^{3} + \frac{1}{x^{3}}\).

A. 24

B. 6

Correct C. 18

D. 12

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 21 View Details

The rational expression \(\frac{x^{2} - p x + q}{x-3}\) can be written in the form \(x + b + \frac{5}{x-3}\), where \(p, q,\) and \(b\) are integers. It is known that \(p\) and \(q\) are positive integers less than 10 and that \(p\) and \(q\) are distinct. Determine the values of \(p, q,\) and \(b\).

A. p = 3, q = 5, b = 1

B. p = 4, q = 5, b = 0

C. p = 3, q = 6, b = 0

Correct D. p = 3, q = 5, b = 0

Correct Answer: D

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 22 View Details

In a school, Class A has 20 students with a mean score of 68 and a sample standard deviation of 5. Class B has 30 students with a mean score of 74 and a sample standard deviation of 6. (a) Verify the overall mean score for the combined 50 students. (b) Assuming the given standard deviations are sample standard deviations, calculate the combined sample standard deviation for all 50 students. Give your answer correct to two decimal places.

A. 6.12

Correct B. 6.31

C. 5.87

D. 7.04

Correct Answer: B

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 23 View Details

The quadratic equation \(x^{2} - (k+4)x + (k+1) = 0\) has two distinct real roots that differ by 2. Find the value of \(k\) and state the two roots.

Correct A. k = 2; roots are 0 and 2

B. k = 2; roots are -1 and 1

C. k = 4; roots are 1 and 3

D. k = -2; roots are -4 and -2

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 24 View Details

A sequence \(\{a_n\}\) is defined by \(a_1 = 3\) and for \(n \ge 1\), \(a_{n+1} = 2a_n + (-1)^n\). Determine the fifth term \(a_5\) and the sum \(S_5 = a_1 + a_2 + a_3 + a_4 + a_5\).

A. a5 = 45, S5 = 85

B. a5 = 39, S5 = 77

Correct C. a5 = 43, S5 = 83

D. a5 = 41, S5 = 81

Correct Answer: C

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Question 25 View Details

Points \(A(2,3)\), \(B(8,5)\) and \(C(5,11)\) are three vertices of a parallelogram \(ABCD\) taken in order. (a) Find the coordinates of the fourth vertex \(D\). (b) Compute the area of the parallelogram. (c) Write the equation of the line through \(D\) that is perpendicular to \(AB\) and state its y‑intercept.

Correct A. D = (-1,9); area = 42; y‑intercept = 6

B. D = (-1,9); area = 36; y‑intercept = 6

C. D = (9,-1); area = 42; y‑intercept = 6

D. D = (-1,9); area = 42; y‑intercept = 8

Correct Answer: A

Want to see the full step-by-step solution? Unlock AI Explanation & Analytics

Master the Exam!

You've seen a preview, but there are thousands more questions plus AI tutor to break down complex solutions.

Unlock Full Access Available for Android & Windows

Help others prepare! Share this practice hub:

Chat with Support