Exam Body

Year

Subject

Paper Type

gce model questions vol1 2023 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 2023 mathematics (Objective) questions designed to simulate the real exam environment.

Practice these randomly selected questions to test your readiness.

Question 1 View Details

The time (T) (in minutes) taken to fill a tank varies directly as the square of the radius (r) of the inlet pipe and inversely as the pressure (P) applied. When (r = 4) cm and (P = 150) kPa, the tank fills in (12) minutes. Find the pressure required to fill the tank in (8) minutes if the radius is increased to (6) cm.

Correct A. 506.25 kPa

B. 225 kPa

C. 337.5 kPa

D. 100 kPa

Correct Answer: A

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

Question 2 View Details

A bag contains red, blue and green balls. The probability of drawing a red ball is twice that of drawing a blue ball, and the probability of drawing a green ball is \(0.1\). A ball is drawn at random, its colour noted, and then the ball is replaced with two balls of the same colour. A second draw is made. What is the probability that the second ball drawn is green?

A. 0.2

B. 0.05

Correct C. 0.1

D. 0.15

Correct Answer: C

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

Question 3 View Details

A cylindrical tank has radius \(10\) cm and height \(h\) cm. From the top of the cylinder a conical frustum of height \(\frac{h}{2}\) cm, with top radius \(5\) cm and bottom radius \(10\) cm, is removed. The remaining volume is \(5000\) cm\(^3\). Find the original height \(h\) of the cylinder (to two decimal places).

A. 20.12 cm

B. 24.78 cm

C. 26.33 cm

Correct D. 22.46 cm

Correct Answer: D

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

Question 4 View Details

The diagram shows the graph of \(y = -x^{2} + 6x - 5\). A horizontal line \(y = c\) cuts the graph at points \(P\) and \(Q\). If the distance \(PQ\) is \(4\) units, find the value of \(c\).

Correct A. 0

B. -2

C. 4

D. 2

Correct Answer: A

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

Question 5 View Details

Let \(a\) and \(b\) be non‑zero numbers such that \(\frac{a}{b} + \frac{b}{a} = 5\). Find the value of \(a^{3} + b^{3}\) expressed in terms of \(ab\).

A. 4\sqrt{7}\,(ab)^{5/2}

B. 4\sqrt{5}\,(ab)^{3/2}

Correct C. 4\sqrt{7}\,(ab)^{3/2}

D. 2\sqrt{7}\,(ab)^{3/2}

Correct Answer: C

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

Question 6 View Details

A monic quadratic equation \(x^{2}+bx+c=0\) has the property that adding 2 to each of its roots yields two numbers that are reciprocals of each other. Given that \(|b|<5\), find the value of \(b+c\).

Correct A. 3

B. 5

C. 2

D. 4

Correct Answer: A

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

Question 7 View Details

The time \(T\) (in minutes) required to paint a wall varies directly with the area \(A\) (in m\(^2\)) and inversely with the number of painters \(P\), but each additional painter beyond the first reduces the overall efficiency by 4% (i.e. the effective number of painters is \(P\times(1-0.04(P-1))\)). When 3 painters paint a wall of area 120 m\(^2\) it takes 40 minutes. How many minutes will it take for 5 painters to paint a wall of area 180 m\(^2\)? Give your answer correct to two decimal places.

Correct A. 39.43

B. 41.00

C. 38.95

D. 40.12

Correct Answer: A

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

Question 8 View Details

The quadratic \(x^{2}+px+12\) is a factor of the cubic \(x^{3}+6x^{2}+qx+24\). Determine the values of \(p\) and \(q\).

A. p=2, q=12

B. p=-3, q=15

C. p=6, q=24

Correct D. p=4, q=20

Correct Answer: D

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

Question 9 View Details

A closed cylindrical can must hold exactly 5000 cm\(^3\) of liquid. The material for the curved side costs twice as much per cm\(^2\) as the material for each of the two circular ends. Determine the radius and the height (in cm) that minimise the total material cost. Give your answers correct to two decimal places.

A. radius = 13.00 cm, height = 9.50 cm

B. radius = 10.00 cm, height = 12.50 cm

C. radius = 12.34 cm, height = 10.98 cm

Correct D. radius = 11.68 cm, height = 11.66 cm

Correct Answer: D

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

Question 10 View Details

Find all integer values of \(k\) for which the quadratic equation \(x^{2}-(k+1)x+2k=0\) has two distinct integer roots.

A. 2 or 4

Correct B. 0 or 6

C. 1 or 5

D. -2 or 8

Correct Answer: B

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

Question 11 View Details

Find all real numbers \(x\) that satisfy both \(\frac{2x-5}{x+3} > 0\) and \(x^{2}-4x+3 < 0\).

Correct A. \(\frac{5}{2}

B. \(\frac{3}{2}

C. \(2

D. \(\frac{5}{2}

Correct Answer: A

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

Question 12 View Details

Let \(x>0\) satisfy \(\log_{2}(x)=\frac{1}{2}\log_{x}8\). Find the value of \(\log_{x}4\).

Correct A. \(\frac{2\sqrt{6}}{3}\)

B. \(\frac{2\sqrt{3}}{3}\)

C. \(\frac{\sqrt{6}}{3}\)

D. \(\frac{2\sqrt{6}}{5}\)

Correct Answer: A

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

Question 13 View Details

In a class of 120 students, 70 study Mathematics, 65 study Physics, and 50 study Chemistry. The numbers studying both Mathematics and Physics, Mathematics and Chemistry, and Physics and Chemistry are 40, 30, and 25 respectively. If 10 students study none of these subjects, how many study all three subjects?

A. 15

B. 25

C. 30

Correct D. 20

Correct Answer: D

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

Question 14 View Details

What is the remainder when \(7^{2023}\) is divided by 10?

A. 1

B. 5

C. 7

Correct D. 3

Correct Answer: D

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

Question 15 View Details

A quadratic function \(f(x)=ax^{2}+bx+c\) passes through the points \((0,4)\), \((2,1)\) and \((5,9)\). Find the value of \(f(3)\).

A. 0

Correct B. 2

C. 4

D. -2

Correct Answer: B

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

Question 16 View Details

Solve for all real numbers \(x\) satisfying \(\left|\frac{2x-5}{x+3}\right|\le 2\).

A. [-\frac{1}{2},\infty)

B. (-\infty,-\frac{1}{4})

Correct C. [\-\frac{1}{4},\infty)

D. [-\frac{1}{4},1)

Correct Answer: C

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 \(S_n = n^{3} - 6n^{2} + 11n\). Find all positive integers \(n\) for which the \(n\)th term \(a_n\) equals 6.

A. 1, 3

B. 4, 5

C. 2, 5

Correct D. 1, 4

Correct Answer: D

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

Question 18 View Details

A fair six‑sided die is rolled. If the result is even, two cards are drawn without replacement from a standard 52‑card deck; if the result is odd, three cards are drawn without replacement. The probability that exactly one of the drawn cards is a heart is \(\frac{2}{5}\). Find the probability that the die shows an even number.

A. 55/91

B. 62/91

Correct C. 61/91

D. 61/85

Correct Answer: C

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

Question 19 View Details

Solve the equation \(\frac{4}{x-1} + \frac{3}{x+2} = 1\) and give the sum of all real solutions.

Correct A. 6

B. 7

C. 8

D. 5

Correct Answer: A

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

Question 20 View Details

A decimal number is \(0.\overline{27}\). After increasing it by \(15\%\), the result is expressed as a fraction in lowest terms. What is the denominator of that fraction?

A. 330

B. 44

C. 110

Correct D. 220

Correct Answer: D

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

Question 21 View Details

A shop offers a 20% discount on the marked price of an item and then a further 10% discount on the reduced price. If the final selling price is \(£72\), what was the original marked price?

A. 90

Correct B. 100

C. 80

D. 110

Correct Answer: B

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

Question 22 View Details

The decimal \(0.27\) is written as a fraction in lowest terms. What is the denominator of that fraction?

A. 10

Correct B. 100

C. 1000

D. 25

Correct Answer: B

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

Question 23 View Details

In the plane, vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 7\). The vector \(\mathbf{c}=2\mathbf{a}-\mathbf{b}\) is perpendicular to \(\mathbf{a}+\mathbf{b}\). Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees (to one decimal place).

A. 102.3

B. 64.0

Correct C. 91.6

D. 78.5

Correct Answer: C

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

Question 24 View Details

The quadratic equation \(x^{2}-kx+(k-6)=0\) has two distinct real roots whose product is 8. Find the value of \(k\) and then give the sum of the squares of the roots.

Correct A. 180

B. 162

C. 144

D. 200

Correct Answer: A

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

Question 25 View Details

In triangle \(ABC\) the side lengths are \(AB = 8\) cm, \(AC = 10\) cm and the area of \(\triangle ABC\) is \(48\) cm\(^2\). Point \(D\) lies on \(BC\) such that \(BD:DC = 2:3\). A line through \(D\) parallel to \(AB\) meets \(AC\) at \(E\). Find the area of \(\triangle CDE\).

A. 432/30

B. 432/20

C. 384/25

Correct D. 432/25

Correct Answer: D

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