Higher Grades 6-7 Mini Test

Question 1 [2 marks]

Ratio and Proportion

P is directly proportional to Q. When Q = 5, P = 30. Find the value of P when Q = 9.

Question 2 [2 marks]

Pythagoras and Trigonometry

Fatima is fencing a triangular flower bed in her garden. Two of the sides measure 1.5 m and 2.3 m, with an angle of 48 degrees between them. Calculate the length of the third side. Give your answer correct to 3 significant figures.

Question 3 [2 marks]

Indices and Standard Form

Evaluate 27^(2/3).

Question 4 [2 marks]

Quadratics

Factorise 3x^2 + 10x + 3

Question 5 [2 marks]

Angles and Geometrical Reasoning

TA is a tangent to a circle at the point A. AB is a chord of the circle, and C is a point on the circle in the alternate segment. The angle between the tangent TA and the chord AB is 63 degrees. Diagram: circle, tangent TA drawn touching at A, chord AB drawn, angle between TA and AB marked 63 degrees at A, point C marked on the circle in the alternate segment, angle ACB marked at C. Write down the size of angle ACB, giving a reason for your answer.

Question 6 [2 marks]

Graphs and Coordinates

A line has gradient 6. Find the gradient of a line perpendicular to it.

Question 7 [3 marks]

Linear Algebra

Solve (x + 3)/4 + (x - 2)/6 = 5/2

Question 8 [3 marks]

Sequences

A quadratic sequence has constant second difference 8. Its 3rd term is 24 and its 5th term is 60. Find an expression for the nth term.

Question 9 [4 marks]

Number and Calculation

The number A = 2^4 x 3^2 x 5 and the number B = 2^2 x 3^3 x 7. (a) Find HCF(A, B). (b) Find LCM(A, B).

Question 10 [6 marks]

Area, Volume and Measures

A gardener makes a raised flower bed in the shape of a rectangle 6 m by 3 m. At each end she places a semicircular planting area whose diameters are the short side of the rectangle, so the semicircles extend beyond the rectangle. She covers the combined area with turf costing £4.50 per square metre. Work out the total cost of turf to the nearest pound. Show your working.

Question 11 [4 marks]

Fractions, Decimals and Percentages

Which of the following mixed numbers are equal? Explain fully. 1 3/5, 1 9/15, 1 6/10, 1 11/15

Question 12 [3 marks]

Statistics and Probability

A nature reserve covers 5 hectares. To estimate its hare population, 45 hares are caught and tagged in a first sample. In a second sample of 60 hares, 9 are found to be tagged.

Estimate the total number of hares in the reserve.

Work out the population density of hares, in hares per hectare.

Question 13 [3 marks]

Graphs and Coordinates

A has coordinates (-2, 1) and B has coordinates (4, 5). Find the length of AB, giving your answer correct to 3 significant figures.

Question 14 [2 marks]

Statistics and Probability

A researcher estimates there are 420 mice in a barn. She marked 35 mice in the first sample. She wants her second sample to contain exactly 5 marked mice.