O Level Mathematics Practice Questions

Find the exact value of $5,4 \times 0,06$.

Find the exact value of $16,5 - 4,96$.

In the diagram, $AD$ is the diameter of the circle $ABCD$. Chords $BC$ and $CD$ are equal and $C\hat{A}B = 33°$. The side $CD$ is produced to $E$.

At the beginning of an examination the clock in the examination room was set to read 2 p.m. The examination ended at 5 p.m.

At the beginning of an examination the clock in the examination room was set to read 2 p.m. The examination ended at 5 p.m.

Calculate the obtuse angle, in degrees, between the hour hand and the minute hand of a clock at 12.30 p.m.

The table shows the results of the games played by the Gweru Giraffes last season and the points awarded in the League Table.

The table shows the results of the games played by the Gweru Giraffes last season and the points awarded in the League Table.

Solve the inequality $-7 < 2 - 3x \leq 5$.

Express 0,072 as a fraction in its lowest terms.

Express 0,072 as a percentage.

In the diagram, the lines $ABC$ and $PQR$ are parallel. The triangle $AQB$ is equilateral. Given that $Q\hat{R}B = 37°$, calculate $R\hat{B}C$, in degrees.

Express 2,5 mm as a fraction of 50 cm in its lowest terms.

Mary drew the pie chart shown to illustrate the time she spent on her homework in one week. The chart shows Mathematics as a right angle (90°), Science as $50°$, English as $3x°$ and Other subjects as $(60+x)°$. Calculate the value of $x$.

Evaluate, giving your answer in decimal form, $1,549 - 0,07267$.

In the diagram, A, B and C are three overlapping sets drawn inside a rectangle representing the universal set. Use set notation to describe the shaded region shown in the diagram.

Giving your answer as a common fraction in its lowest terms, find the value of $7\frac{2}{5} - 6\frac{2}{3}$.

Evaluate, giving your answer as a common fraction in its lowest terms: $\frac{3}{4} + \frac{1}{5}$.

Express 30,098 correct to the nearest tenth.

Express one million and one in figures.

Express 4,695 to 2 decimal places.

Express 54,497 correct to the nearest tenth.

Simplify $0 - (-3)$.

Evaluate $-2 + 3 \times 4 - 4$.

For the graph of y = x^3, calculate the value of y when x = 2,5.

The lines y = 100 and 10x + 7y = 2000 are drawn on the same axes. Calculate the coordinates of the point where they cross.

The lines y = 1 and x + y = 5 are drawn on the same axes. Calculate the coordinates of the point where they cross.

The lines x = 20 and x = 2y are drawn on the same axes. Calculate the coordinates of the point where they cross.

Answer the whole of this question on a sheet of plain paper. Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be done on a single diagram. (a) Construct a quadrilateral ABCD in which AB = 8,5 cm, AD = 7 cm, DC = 5 cm, angle ADC = 90 degrees and angle BAD = 60 degrees. [6] (b) Measure and write down the length of BC. [1] (c) Construct the locus of a point (i) that is 4,5 cm from B, (ii) X, on the same side of AD as C, such that the area of triangle ACD = area of triangle AXD. [3] (d) Mark and label X1 and X2, the points that are 4,5 cm from B and are such that the area of triangle AX1D = the area of triangle AX2D. [2]

A car tank holds 22 1/2 litres of fuel when it is 3/8 full. Calculate the amount of fuel when it is full.

In the diagram, ABC is an isosceles triangle with AB = AC and angle ABC = 68°. ACD is parallel to PBQ. Calculate (i) angle BCD, (ii) angle PBA.

(a) Write down the special name given to a polygon with five sides. [1] (b) State, for a regular five-sided polygon, (i) the number of lines of symmetry, [1] (ii) the order of rotational symmetry. [1]

The lines y = x and x + y = 60 are drawn on the same axes. Calculate the coordinates of the point where they cross.

Use ruler and compasses only for all constructions and show clearly all the construction lines and arcs. (a) On a single diagram, construct (i) triangle PQR in which PR = 9 cm, PQ = 7 cm and angle QPR = 45 degrees, [3] (ii) the locus of points which are equidistant from PQ and PR, [2] (iii) the locus of points which are equidistant from P and Q, [2] (iv) mark and label clearly, the point X which is equidistant from PQ and PR and is also equidistant from P and R. [1] (b) Measure and write down (i) the length of XR, [1] (ii) angle PRQ. [1]

The diagram shows a trough in the form of a prism whose cross section ABCD is a trapezium with AD parallel to BC and the measurements are in centimetres. AD = 40, BC = 21, AB = 18, the perpendicular height from BC to AD is 14 and the trough is 90 long. (a)(i) Calculate the area of the cross-section ABCD of the trough. (ii) Calculate the capacity of the trough when full. (b) The inside of the trough is to be painted. One litre of the paint covers an area of 1 496 cm^2. (i) Calculate the area of the trough to be painted. (ii) Calculate the number of litres of paint needed to paint the inside of the trough to the nearest litre. (iii) Calculate the cost of the paint if one litre of the paint costs $6,30.

In the diagram, MNC is a triangle in which angle MNC = 64°. A is a point inside the triangle such that AM = AC, angle AMN = 42°, angle ACN = 26°, angle AMC = x° and angle CAM = y°. (i) Find the value of y, [2] (ii) Find the value of x. [2]

(b) Find the Highest Common Factor (H.C.F) of 2^3 x 3^2 x 5 x 7^4, 2^3 x 3^3 x 5^2 x 7^2, 2^4 x 3 x 5 x 7^3, leaving the answer in index form. (c) Find the Lowest Common Multiple (L.C.M) of 3x^2y, 5x^3y^2 and 8xy^3.

Use pencil, ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be on a single diagram. (a) (i) Construct, in a single diagram, triangle AXB such that AX = 5 cm, BX = 7,5 cm and angle AXB = 60 degrees. [3] (ii) Construct the locus of points which are 1. equidistant from XA and XB, [2] 2. 3,5 cm from X. [1] (iii) Show by shading, the region R, in the triangle, such that R is closer to XA than XB and XR is less than or equal to 3,5 cm. [2] (b) Measure and write down the length of AB. [1]

In the diagram, OQR, OMP, PTQ and RTM are straight lines such that OM = (1/3)OP and PT = (3/4)PQ. It is given that OP = 12a and OQ = 4b. (a) Express as simply as possible, in terms of a and/or b (i) PQ, [1] (ii) PT, [1] (iii) OT, [1] (iv) MT. [2] (b) It is given that MR = h MT. Express OR in terms of a and/or b and a constant h. [2] (c)(i) It is given that OR = k OQ. Express OR in terms of a and/or b and a constant k. [1] (ii) Use the expressions for OR in (b) and (c)(i) to find the values of h and k. [3] (d) Write down the numerical value of MT:TR. [1]

On a graph the boundary of the region defined by the inequality y > 5 is drawn as a broken line rather than a solid one. State the largest integer value of y that does not satisfy y > 5.

It is given that P is a proper subset of Q and Q is a proper subset of R. Write down, in their simplest forms, the sets R intersect P and P union Q, giving the answer as 'first, second'.

(a) Write down the next term in the sequence below. 1/3 ; 2/4 ; 3/5 ; 4/6 ; ___ [1] (b) Express 10 as a sum of two different prime numbers. [1]

The diagram shows the cross-section of a garden shed. The cross-section ABCDE is made up of a rectangle measuring 2 m by 2,2 m and an isosceles triangle with a perpendicular height of 0,6 m and a base of 2 m. (a) Calculate the area of the cross-section. (b) If the shed is 3 m long, calculate the volume of the shed. (c) It is given that 23 m^2 of the surface area of the shed need to be painted and that one tin of paint covers an area of 4,5 m^2. Calculate the number of tins of paint that have to be bought to cover the 23 m^2. (d)(i) Calculate the length of the edge DE. (ii) The sloping roof is to be covered by roofing material which costs $6.40 per square metre. Calculate the cost of roofing material needed to cover the sloping roof.

Use ruler and compasses only for all constructions and show clearly all construction lines and arcs. All constructions should be done in a single diagram. ABCD is a trapezium in which AB = 6,5 cm, AD = 5,2 cm, angle ABC = 120 degrees and AD is perpendicular to AB. DC is parallel to AB. (a) (i) Construct the trapezium ABCD. [6] (ii) Construct the bisector of angle ABC. [2] (b) Describe the locus of points that the bisector of angle ABC represents. [2] (c) Measure and write down the length of BC. [1]

Remove brackets and simplify the expression $3(5 - x) - 2x(x + 3)$.

Integers $x$, $y$ and $z$ are such that $x \le 6$, $y \ge -2$ and $-6 \le z \le 4$. Find the least possible value of $yz^2$.

Factorise completely $125p^3 - 5p$.

During a sale, the price of a camera was reduced from $160 to$148,80. Calculate the percentage decrease in price.