Foundation Grade 4 Mini Test B

Question 1 [2 marks]

Area, Volume and Measures

A sphere has radius 6 cm. Calculate the volume of the sphere. Give your answer correct to 3 significant figures.

Question 2 [2 marks]

Angles and Geometrical Reasoning

A heptagon has 7 sides. Calculate the sum of the interior angles of a heptagon.

Question 3 [1 marks]

Area, Volume and Measures

Two squares are drawn, of any size.

Question 4 [2 marks]

Angles and Geometrical Reasoning

The exterior angle of a regular polygon is 15 degrees. Work out the number of sides of the polygon.

Question 5 [2 marks]

Quadratics

Three students each drew a table of values for y = x^2 - 3x, for -3 <= x <= 3. Only one table is correct.

Which table is correct?

Give a reason for your answer.

Question 6 [2 marks]

Angles and Geometrical Reasoning

A garden sprinkler is placed at point S. It waters the ground up to a distance of 3.5 m from S. Using a scale of 1 cm to 1 m, draw the locus of the boundary of the area that gets watered.

Question 7 [1 marks]

Statistics and Probability

A class of 24 students was asked whether they study French (F) or Spanish (S). The Venn diagram shows: French only = 6, both French and Spanish = 4, Spanish only = 9, and neither = 5. Write down the number of students who study both French and Spanish.

Question 8 [2 marks]

Angles and Geometrical Reasoning

A solid is built from 1 cm cubes. It is 4 cubes long and 2 cubes deep. In every column of cubes, the height is the same in the back row as it is in the front row. Four diagrams show possible front elevations, each 4 squares wide. The numbers show the height, in unit squares, of each column, left to right. A) 1, 1, 2, 2 B) 2, 2, 1, 1 C) 2, 1, 1, 2 D) 1, 2, 2, 1 The solid's two tallest columns (height 2) are on the left, and its two shortest columns (height 1) are on the right.

Which diagram, A, B, C or D, is the correct front elevation of the solid?

How many unit cubes make up the whole solid?

Question 9 [3 marks]

Pythagoras and Trigonometry

The diagram shows a right-angled triangle ABC, with the right angle at B and angle theta marked at vertex A. Diagram: right-angled triangle ABC, right angle marked at B, angle theta marked at A, side AB along the base, side BC vertical, side AC the sloping side joining A to C.

Write down the letter of the side that is the hypotenuse.

Write down the letter of the side that is opposite angle theta.

Write down the letter of the side that is adjacent to angle theta.

Question 10 [3 marks]

Angles and Geometrical Reasoning

A solid is built from unit cubes on a 2 by 2 grid. Let the positions be Front-left, Front-right, Back-left and Back-right. The front elevation viewed from the front shows heights (left to right) 2 and 1. The side elevation viewed from the right shows heights (front to back) 2 and 1. Work out the height (number of unit cubes stacked) at each of the four grid positions.

Question 11 [3 marks]

Area, Volume and Measures

A cylinder has height 10 cm and volume 1256 cm^3. Work out the radius of the cylinder. Give your answer to 1 decimal place.

Question 12 [3 marks]

Angles and Geometrical Reasoning

Describe the steps to construct, with compass and straightedge, the perpendicular from a point P to a given line l (P not on l). Explain briefly why the construction produces a right angle.

Question 13 [4 marks]

Sequences

Special sequences of numbers include square numbers and triangular numbers.

Write down the first five square numbers.

Write down the first five triangular numbers.

The nth triangular number is given by the formula n(n + 1) / 2. Use this formula to find the 12th triangular number.

Question 14 [4 marks]

Angles and Geometrical Reasoning

The diagram shows a solid built from 1 cm cubes standing on a grid. The numbers show how many cubes are stacked at each position.

Draw the front elevation of the solid, as viewed from arrow F.

Draw the side elevation of the solid, as viewed from arrow S.

Question 15 [6 marks]

Area, Volume and Measures

The diagram shows a shape made from a rectangle measuring 12 cm by 8 cm, with a semicircle of diameter 8 cm attached to one of the 8 cm ends.

Work out the perimeter of the shape. Give your answer correct to 1 decimal place.

Work out the area of the shape. Give your answer correct to 1 decimal place.