Higher Grades 4-5 Mini Test

Question 1 [3 marks]

Number and Calculation

Priya is choosing a meal at a restaurant. The menu has 3 starters, 5 main courses and 2 desserts. She chooses exactly one starter, one main course and one dessert.

Work out the number of different three-course meals Priya could choose.

The restaurant adds one extra starter to the menu. Work out the new number of different three-course meals possible.

Question 2 [1 marks]

Indices and Standard Form

Four students each write the number 84000 in standard form. Amir writes 8.4 x 10^4 Ben writes 84 x 10^3 Chloe writes 0.84 x 10^5 Dev writes 8.4 x 10^3 Exactly one student has written the number correctly in standard form. Write down the name of that student.

Question 3 [2 marks]

Pythagoras and Trigonometry

In a right-angled triangle the two shorter sides are 9 cm (adjacent to angle B) and 12 cm (opposite to angle B). Without using Pythagoras, find angle B by using tan. Give your answer to 1 decimal place.

Work out tan B then find B to 1 decimal place.

Question 4 [2 marks]

Fractions, Decimals and Percentages

Leah invests £400 in a savings account that pays compound interest at a rate of 5% per year. Work out the value of her investment at the end of 2 years.

Question 5 [2 marks]

Linear Algebra

Make x the subject of the formula: y = 4x - 3z

Question 6 [2 marks]

Quadratics

Factorise fully: x^2 + 5x - 14.

Question 7 [2 marks]

Sequences

Find the nth term of the sequence 8, 21, 40, 65.

Question 8 [2 marks]

Linear Algebra

Solve 20 - 3x = 5

Question 9 [3 marks]

Ratio and Proportion

Amira and Ben share £96 in the ratio 5 : 3. Work out how much each person receives.

Question 10 [3 marks]

Statistics and Probability

A gardener records the height of a plant each week. Number of weeks (x): 1, 2, 3, 4, 5, 6, 7, 8. Height of plant in cm (y): 5, 9, 14, 17, 22, 26, 29, 34. The points for weeks 1 to 6 have already been plotted on the grid.

Plot the remaining two points from the table on the grid.

State the type of correlation shown.

Question 11 [3 marks]

Area, Volume and Measures

A solid hemisphere has radius 6 cm. Work out the total surface area of the hemisphere (curved surface plus the flat circular face). Give your answer correct to 3 significant figures.

Question 12 [3 marks]

Statistics and Probability

A gardener plants 4 sunflower seeds. Each seed germinates independently with probability 0.9. Find the probability that at least one of the seeds fails to germinate.

Question 13 [4 marks]

Angles and Geometrical Reasoning

The front elevation of a garden summerhouse is a rectangle with an isosceles triangle roof on top. The rectangle is 3.2 m wide and 2.1 m high. The triangular roof has a base of 3.2 m and a height of 0.9 m. Work out the total area of the front elevation.

Question 14 [4 marks]

Area, Volume and Measures

A circular pizza has a diameter of 32 cm. Fatima cuts a slice which forms a sector with an angle of 45 degrees at the centre.

Calculate the length of the curved crust edge of the slice, giving your answer correct to 3 significant figures.

Calculate the area of the slice, giving your answer correct to 3 significant figures.

Question 15 [4 marks]

Graphs and Coordinates

Find the gradient of the line perpendicular to 4x + 2y = 6. Then give the equation of that perpendicular line which passes through (3, -2).

Give the equation of the perpendicular line through (3, -2).