Exam Body

Year

Subject

Paper Type

gce model questions vol1 2017 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 2017 mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

Triangle ABC is right‑angled at C. Its perimeter is 60 cm and its area is 150 cm². Find the radius of the inscribed circle (in cm).

Correct A. 5

B. 8

C. 6

D. 4

Correct Answer: A

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

Question 2 View Details

In triangle ABC, AB = 8 cm and AC = 6 cm. The altitude from B meets AC at D such that AD = 3 cm. Find the measure of angle \(\angle BAC\) correct to the nearest degree.

A. 75°

B. 60°

Correct C. 68°

D. 72°

Correct Answer: C

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

Question 3 View Details

Solve for \(x\): \(|3x - 7| = 2x + 1\).

A. x = 8 or x = -6/5

B. x = -8 or x = 6/5

C. x = 8 or x = 5/6

Correct D. x = 8 or x = 6/5

Correct Answer: D

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

Question 4 View Details

The quadratic equation \(x^{2}-(k+1)x+k=0\) has integer roots, one of which is exactly twice the other. Find the value of \(k\).

A. 1

Correct B. 2

C. 4

D. 3

Correct Answer: B

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

Question 5 View Details

In a school, 120 students study at least one of Mathematics (M), Physics (P) or Chemistry (C). The numbers are: \(|M| = 70\), \(|P| = 65\), \(|C| = 50\). The numbers studying both subjects are: \(|M\cap P| = 30\), \(|M\cap C| = 25\), \(|P\cap C| = 20\). How many students study all three subjects?

Correct A. 10

B. 15

C. 20

D. 5

Correct Answer: A

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

Question 6 View Details

In the coordinate plane the points A(1, 2) and C(8, 7) are shown. Point B lies on the line through A with gradient \( \frac{3}{2} \). If the area of triangle \( \triangle ABC \) is \(24\) square units, find the possible coordinates of B.

Correct A. [(-85/11, -122/11), (107/11, 166/11)]

B. [(-90/11, -130/11), (100/11, 150/11)]

C. [(-85/11, -122/11), (107/11, 160/11)]

D. [(-84/11, -120/11), (108/11, 168/11)]

Correct Answer: A

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

Question 7 View Details

A line passes through the points \((2, k)\) and \((5, 8)\). Another line has equation \(3x - 4y = 12\). If the sum of the x‑intercepts of the two lines is \(10\), determine the value of \(k\) and then find the coordinates of the intersection of the two lines.

A. (k = 32, intersection = (204/35, 50/35))

B. (k = 28, intersection = (210/35, 50/35))

Correct C. (k = 32, intersection = (204/35, 48/35))

D. (k = 30, intersection = (200/35, 45/35))

Correct Answer: C

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

Question 8 View Details

Simplify the expression \[ \frac{x^{2}-6x+9}{x-3}+\frac{2x-4}{x^{2}-4x+4} \] and, given that \(x\) satisfies \((x-1)(x-5)=4\), find the possible values of the simplified expression.

A. [ (16*sqrt(2)-2)\/7 , -(16*sqrt(2)+2)\/7 ]

B. [ (18*sqrt(2)-4)\/7 , -(18*sqrt(2)+4)\/7 ]

C. [ (18*sqrt(2)+2)\/7 , -(18*sqrt(2)-2)\/7 ]

Correct D. [ (18*sqrt(2)-2)/7 , -(18*sqrt(2)+2)/7 ]

Correct Answer: D

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

Question 9 View Details

Real numbers \(a\) and \(b\) satisfy \(a+b=5\) and \(a^{2}+b^{2}=13\). Evaluate \[ G = \frac{a^{3}-b^{3}}{a-b}+ab .\]

A. 20

Correct B. 25

C. 30

D. 13

Correct Answer: B

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

Question 10 View Details

Solve for \(x\) (in degrees) with \(0^{\circ}<x<180^{\circ}\) satisfying \[ 2\sin^{2}x-\sqrt{3}\sin 2x = 1 .\] List all possible values of \(x\).

A. [45°, 135°]

B. [15°, 105°]

Correct C. [75°, 165°]

D. [30°, 150°]

Correct Answer: C

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

Question 11 View Details

The three‑digit integer \(3AB\) (where \(A\) and \(B\) are digits) is divisible by 9. What is the smallest possible value of \(A+B\)?

A. 9

Correct B. 6

C. 12

D. 5

Correct Answer: B

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

Question 12 View Details

The speed-time graph of a car is described as follows: from \(t=0\) s to \(t=4\) s the speed increases uniformly from \(0\) to \(8\) m s\(^{-1}\); from \(t=4\) s to \(t=7\) s the speed remains constant at \(8\) m s\(^{-1}\); from \(t=7\) s to \(t=10\) s the speed decreases uniformly to \(2\) m s\(^{-1}\). Find the total distance travelled by the car between \(t=0\) s and \(t=10\) s. Give your answer in metres.

A. 70

B. 60

Correct C. 55

D. 45

Correct Answer: C

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

Question 13 View Details

A sum of money is increased by 20 % and then reduced by 10 % of the increased amount. The final amount is £108. What was the original sum (in pounds)?

A. 120

B. 90

C. 110

Correct D. 100

Correct Answer: D

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

Question 14 View Details

Find the smallest integer \(k\) such that \(|2x-5| < k\) holds for every real number \(x\) satisfying \(1 \le x \le 4\).

A. 5

Correct B. 4

C. 3

D. 6

Correct Answer: B

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

Question 15 View Details

The first three terms of a sequence are \(2,\;6,\;12\). Each term can be expressed as the product of its position \(n\) and the next integer, i.e. \(a_n = n(n+1)\). Assuming this pattern continues, find the sixth term of the sequence.

A. 36

Correct B. 42

C. 56

D. 48

Correct Answer: B

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

Question 16 View Details

The base‑5 number \(132_5\) is converted to decimal and then doubled. The resulting decimal number, when expressed again in base 5, is \(314_5\). What is the decimal value of \(132_5\)?

Correct A. 42

B. 39

C. 45

D. 48

Correct Answer: A

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

Question 17 View Details

The decimal \(0.\overline{27}\) can be written as a fraction \(\frac{p}{q}\) in lowest terms. Find the value of \(p+q\).

A. 16

B. 13

Correct C. 14

D. 15

Correct Answer: C

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

Question 18 View Details

In triangle \(ABC\) the side lengths are \(AB=13\text{ cm}\), \(AC=15\text{ cm}\) and \(BC=14\text{ cm}\). Find the length of the internal angle bisector from vertex \(A\) to side \(BC\).

A. (3\sqrt{61})/2 cm

B. (5\sqrt{13})/2 cm

Correct C. (3\sqrt{65})/2 cm

D. (3\sqrt{65})/3 cm

Correct Answer: C

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

Question 19 View Details

Solve the system of inequalities \(\displaystyle \frac{|2x-5|}{x-3}<2\) and \(x^{2}-4x+3\le 0\). Express the solution set for \(x\).

A. 1 < x < 3

B. 0 \le x < 3

Correct C. 1 \le x < 3

D. 1 \le x \le 2

Correct Answer: C

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

Question 20 View Details

Class A has 20 students with a mean score of 68. Class B has 20 students with a mean score of 76, so the overall mean of the 40 students is 72. After a retest, each of the five lowest‑scoring students in class B improves by the same number of marks, and as a result the overall mean rises to 73. It is also known that after the improvement each of those five students has a score equal to the original overall mean (72). Find the original mean score of those five students.

Correct A. 64

B. 66

C. 62

D. 70

Correct Answer: A

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

Question 21 View Details

Simplify the expression \( \dfrac{2^{3}\,\sqrt{8}}{4^{\frac{3}{2}}} \).

Correct A. 2\sqrt{2}

B. 4\sqrt{2}

C. \sqrt{2}

D. 2\sqrt{3}

Correct Answer: A

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

Question 22 View Details

A bag contains 6 white and 4 black balls. Another bag contains 3 white and 7 black balls. One bag is chosen at random and two balls are drawn without replacement from the chosen bag. Given that the two drawn balls are of the same colour, find the probability that the first bag was chosen.

Correct A. 7/15

B. 3\/7

C. 5\/12

D. 2\/5

Correct Answer: A

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

Question 23 View Details

From the numbers 1 to 12 a pair of distinct numbers is drawn at random without replacement. Given that at least one of the drawn numbers is a multiple of 3, find the probability that the sum of the two numbers is odd.

Correct A. 10/19

B. 10/18

C. 9/19

D. 11/19

Correct Answer: A

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

Question 24 View Details

Find the centre and radius of the circle that passes through the points \(A(1,2)\) and \(B(4,6)\) and whose centre lies on the line \(x+2y=5\).

A. Centre \((23\/2, -17\/4)\); radius \(\frac{20\sqrt{5}}{4}\)

B. Centre \((27\/2, -17\/4)\); radius \(\frac{30\sqrt{5}}{4}\)

C. Centre \((27\/2, -13\/4)\); radius \(\frac{25\sqrt{5}}{4}\)

Correct D. Centre \((27/2, -17/4)\); radius \(\frac{25\sqrt{5}}{4}\)

Correct Answer: D

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

Question 25 View Details

Let \(x\) and \(y\) be non‑zero real numbers satisfying \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{2}\) and \(xy=12\). Find the value of \(\dfrac{x^{2}+y^{2}}{xy}\).

A. 0

Correct B. 1

C. 2

D. 3

Correct Answer: B

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