Higher Grades 5-6 Mini Test

Question 1 [1 marks]

Quadratics

Factorise x^2 - 49

Question 2 [2 marks]

Number and Calculation

A cafe sells sandwiches with a choice of 4 types of bread and 3 types of filling. Each sandwich has exactly one type of bread and one filling. Work out the total number of different sandwiches possible.

Question 3 [1 marks]

Ratio and Proportion

Given that y = 3/5 x, write down the ratio x:y in its simplest form.

Question 4 [1 marks]

Angles and Geometrical Reasoning

Point R has coordinates (6, -1). Write down the coordinates of the image of R after a reflection in the line y = x.

Question 5 [2 marks]

Indices and Standard Form

Show that (6 + sqrt(7))(6 - sqrt(7)) = 29.

Question 6 [2 marks]

Pythagoras and Trigonometry

In triangle YZA, angle Y = 96 degrees, ZA = 15.2 cm (opposite angle Y), and YA = 8.6 cm (opposite angle Z). Calculate the size of angle Z. Give your answer correct to 1 decimal place.

Question 7 [2 marks]

Statistics and Probability

Using the same table as Question 7 (time, t minutes, spent on homework by 30 pupils): Time, t (minutes): 0 < t <= 20, 20 < t <= 40, 40 < t <= 60, 60 < t <= 80, 80 < t <= 100 Frequency (f): 4, 9, 11, 4, 2 Total number of pupils = 30 State the class that contains the median.

Question 8 [2 marks]

Linear Algebra

Factorise x^2 + 3x - 40

Question 9 [2 marks]

Fractions, Decimals and Percentages

£250 is invested for 3 years at a rate of 2% per year compound interest. Work out the value of the investment at the end of 3 years, giving your answer to the nearest penny.

Question 10 [3 marks]

Graphs and Coordinates

Without using a calculator, write down the exact value of each of the following.

sin 30 degrees

cos 60 degrees

tan 45 degrees

Question 11 [3 marks]

Linear Algebra

Solve the simultaneous equations: 4x + y = 5 2x - 3y = 13

Question 12 [3 marks]

Angles and Geometrical Reasoning

O is the origin. The position vectors of A and B, relative to O, are a and b. P lies on AB such that AP : PB = 2 : 3. Find the position vector of P, OP, in terms of a and b, giving your answer in its simplest form.

Question 13 [4 marks]

Area, Volume and Measures

A sector of a circle has radius 9 cm and angle 120 degrees. Work out the length of the arc of the sector. Give your answer in terms of pi.

Question 14 [5 marks]

Angles and Geometrical Reasoning

PA and PB are tangents to a circle with centre O, touching the circle at A and B respectively. Angle APB = 50 degrees. Diagram: circle, centre O, external point P, tangents PA and PB drawn touching the circle at A and B, radii OA and OB drawn, right angles marked at A and B, angle APB = 50 degrees marked at P.

Work out the size of angle AOB.

Work out the size of angle OAB.

Question 15 [7 marks]

Sequences

Arjun is training for a marathon. In week 1, he runs 8 km. Each week after that, he runs 3 km more than the week before.

Work out how far Arjun runs in week 6.

Find an expression, in terms of n, for the distance, in km, Arjun runs in week n.

Arjun wants to know the first week in which he will run at least 50 km. Find this week number.