Exam Body

Year

Subject

Paper Type

igcse model questions vol1 2017 mathematics | Objective

Prepare for your exams with igcse 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

A three‑digit integer has the property that when its digits are reversed the resulting three‑digit number is 297 less than the original. Find the original integer.

Correct A. 401

B. 603

C. 502

D. 704

Correct Answer: A

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

Question 2 View Details

In the diagram, a straight line passes through the points \((2,3)\) and \((8,k)\). The line meets the x‑axis at point \(A\) and the y‑axis at point \(B\). The triangle formed by the origin \(O\) and the intercepts \(A\) and \(B\) has area \(24\) square units. Find the value of \(k\).

Correct A. 18\sqrt{2} - 24

B. 24 - 18\sqrt{2}

C. 12\sqrt{2} - 24

D. 18\sqrt{2} + 24

Correct Answer: A

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

Question 3 View Details

A box contains some white and black balls. Initially there are 5 white balls and an unknown number of black balls. A ball is drawn at random, its colour noted, and then it is replaced together with two additional balls of the same colour. A second draw is then made from the enlarged collection. The probability that both drawn balls are white is \(\frac{35}{48}\). Find the total number of balls that were originally in the box.

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 4 View Details

A student guesses on each of 10 independent multiple‑choice questions, each having four options. The probability of guessing a question correctly is \(0.2\). Find, correct to four decimal places, the probability that the number of correctly answered questions is a prime number.

A. 0.5405

Correct B. 0.5305

C. 0.5205

D. 0.5315

Correct Answer: B

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

Question 5 View Details

Simplify \(\displaystyle \frac{(2^{3}\cdot5^{2})^{\frac12}}{\sqrt{20}}\) and express your answer in simplest surd form.

Correct A. \sqrt{10}

B. 2\sqrt{5}

C. \sqrt{5}

D. \sqrt{20}

Correct Answer: A

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

Question 6 View Details

A point P(3,1) is reflected in the line \(y = kx\) (where \(k\) is a constant). The image is then rotated 90° anticlockwise about the origin. After these two transformations the resulting point is translated by the vector \((3, -1)\) to give the point Q(8,4). Find the value of \(k\).

A. \frac{1}{2}

Correct B. -\frac{1}{2}

C. -\frac{1}{3}

D. -\frac{2}{1}

Correct Answer: B

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

Question 7 View Details

A quadratic function \(y = ax^{2} + bx + c\) passes through the points \((1,2)\) and \((3,10)\). Its vertex lies on the line \(y = 2x - 1\). Find the value of \(a\).

A. 4

B. -1

Correct C. 3

D. 2

Correct Answer: C

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

Question 8 View Details

A rectangular box has length twice its width. Its total surface area is \(156\ \text{cm}^{2}\) and its volume is \(120\ \text{cm}^{3}\). Find the height of the box in centimeters, giving your answer as a fraction in lowest terms.

Correct A. \frac{20}{3}

B. \frac{7}{2}

C. \frac{25}{4}

D. \frac{15}{2}

Correct Answer: A

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

Question 9 View Details

A class of 30 students took two examinations, A and B. The mean score for exam A is 68 and for exam B is 72. The overall mean of all 60 scores is 70. The sum of squared deviations from the mean for exam A is 540 and for exam B is 720. Find the combined standard deviation of all 60 scores, giving your answer to two decimal places.

A. 4.47

B. 6.12

Correct C. 5.00

D. 5.83

Correct Answer: C

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

Question 10 View Details

A bag contains 4 red, 5 blue and 6 green balls. Two balls are drawn successively without replacement. (a) Find the probability that the two balls are of different colours given that at least one of the drawn balls is red. (b) Find the probability that both balls are blue given that at least one of the drawn balls is blue. Give your answers in lowest terms.

A. (a) 23/25, (b) 11/69

B. (a) 18/25, (b) 9/69

C. (a) 19/25, (b) 12/69

Correct D. (a) 22/25, (b) 10/69

Correct Answer: D

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

Question 11 View Details

In triangle \(PQR\), the vertices are \(P(1,2)\), \(Q(7,y)\) and \(R(x,5)\). The centroid \(G\) of the triangle lies on the line \(2x - y = 3\). Moreover, the triangle is right‑angled at \(P\). Find the product \(xy\).

A. 5

B. 3

C. 1

Correct D. 2

Correct Answer: D

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

Question 12 View Details

In triangle \(ABC\), side \(a = BC = 13\) cm and side \(b = CA = 14\) cm. The altitude from vertex \(C\) to side \(AB\) has length \(12\) cm. Determine \(\angle C\) (in degrees) correct to one decimal place.

Correct A. 53.7

B. 45.0

C. 60.0

D. 70.2

Correct Answer: A

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

Question 13 View Details

The sum of the first \(n\) terms of an arithmetic progression (AP) equals the sum of the first \(n\) terms of a geometric progression (GP). Both progressions have first term \(3\). The AP has integer common difference \(d\) and the GP has common ratio \(r\) (\(r \neq 1\)). Given that \(n>1\), find the common ratio \(r\) and the \(n\)th term of the AP.

A. r = 3, nth term = 11

B. r = 2, nth term = 13

Correct C. r = 2, nth term = 11

D. r = 4, nth term = 15

Correct Answer: C

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

Question 14 View Details

Simplify \(\displaystyle \frac{2^{5}\,\sqrt{8}}{4^{2}\,\sqrt{2}}\) and give your answer as an integer.

A. 2

B. 8

Correct C. 4

D. 16

Correct Answer: C

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

Question 15 View Details

The volume \(V\) of an ideal gas varies directly with the amount of substance \(n\) and the temperature \(T\), and inversely with the pressure \(P\) (\(V = k\,\frac{nT}{P}\)). At a certain condition, 2 mol of gas at 300 K and pressure 1 atm occupy 49.2 L. Using this information, calculate the volume occupied by 5 mol of the gas at 350 K and pressure 0.8 atm. Give your answer to one decimal place.

A. 143.5

B. 182.0

Correct C. 179.4

D. 153.8

Correct Answer: C

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

Question 16 View Details

In a class of 150 students, 80 study Mathematics, 70 study Physics, and 60 study Chemistry. The numbers who study both Mathematics and Physics, Physics and Chemistry, and Mathematics and Chemistry are 40, 30, and 20 respectively. Exactly 10 students study none of these subjects. How many students study all three subjects?

A. 40

B. 30

C. 10

Correct D. 20

Correct Answer: D

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

Question 17 View Details

In triangle \(ABC\), \(AB = 8\) cm, \(AC = 6\) cm. The altitude from \(A\) meets side \(BC\) at \(D\) such that \(BD:DC = 3:2\). Find \(\sin \angle ABC\).

Correct A. \sqrt{\frac{17}{80}}

B. \sqrt{\frac{17}{64}}

C. \sqrt{\frac{9}{80}}

D. \sqrt{\frac{25}{80}}

Correct Answer: A

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

Question 18 View Details

If \(x\) satisfies \(2x^{2} - 5x + 2 = 0\), evaluate the sum of the two values of \(\displaystyle \frac{3x^{3} - 4x^{2} + x}{x^{2} - 1}\) corresponding to the two roots of the equation.

A. 7\/3

B. 9\/2

C. 5\/2

Correct D. 7/2

Correct Answer: D

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

Question 19 View Details

The first three terms of an arithmetic progression are \(a,\ a+d,\ a+2d\). The sum of these three terms is \(45\) and the sum of the next three terms (\(a+3d,\ a+4d,\ a+5d\)) is \(81\). Find the sixth term of the progression.

A. 29

Correct B. 31

C. 35

D. 33

Correct Answer: B

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

Question 20 View Details

In the diagram, points \(P(1,2)\) and \(Q(7,8)\) are the endpoints of a diameter of a circle. Point \(S(10,5)\) lies outside the circle. From \(S\) a tangent touches the circle at point \(T\). Determine the coordinates of \(T\).

A. (4,5) and (4,2)

B. (7,5) and (7,0)

C. (1,2) and (1,8)

Correct D. (7,8) and (7,2)

Correct Answer: D

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

Question 21 View Details

Two vectors \(\mathbf{a}\) and \(\mathbf{b}\) lie in the same plane. Their magnitudes are \(|\mathbf{a}| = 5\) and \(|\mathbf{b}| = 8\). It is known that the vector \(\mathbf{a} + 2\mathbf{b}\) is perpendicular to the vector \(3\mathbf{a} - \mathbf{b}\). Find the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees, correct to one decimal place.

A. 90.0

B. 120.5

Correct C. 74.6

D. 45.0

Correct Answer: C

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

Question 22 View Details

The quadratic equation \(x^{2} - kx + 12 = 0\) has roots that are the reciprocals of the roots of the quadratic equation \(x^{2} - 7x + m = 0\). Find the value of \(k + m\).

A. 1010/12

Correct B. 1009/12

C. 1008/12

D. 1009/13

Correct Answer: B

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

Question 23 View Details

A garden has the shape of a rectangle with a semicircular end. The length of the rectangular part (excluding the semicircle) is twice its width. The diameter of the semicircle equals the width of the rectangle. If the perimeter of the whole garden is \(60\) m, calculate the area of the garden in square metres, correct to one decimal place.

A. 210.5

B. 185.3

C. 172.9

Correct D. 199.7

Correct Answer: D

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

Question 24 View Details

When the integer \(7\,654\,321\) is divided by \(9\), what is the remainder?

A. 0

B. 8

C. 2

Correct D. 1

Correct Answer: D

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

Question 25 View Details

Vectors \(\mathbf{a}\) and \(\mathbf{b}\) satisfy \(|\mathbf{a}| = 5\) cm, \(|\mathbf{b}| = 7\) cm and \(|\mathbf{a} + 2\mathbf{b}| = 13\) cm. Determine the angle between \(\mathbf{a}\) and \(\mathbf{b}\) in degrees, rounded to the nearest whole number.

Correct A. 112

B. 95

C. 68

D. 130

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