Practice Tests
Part 1: Pythagoras’ Theorem
1. True or False: Pythagoras' Theorem applies to all triangles.
2. In a right-angled triangle, one side is 6 cm, the other side is 8 cm, and the hypotenuse is unknown. Calculate the hypotenuse.
3. A right triangle has a hypotenuse of 13 cm and one side of 5 cm. Find the length of the other side.
Part 2: Equations
4. Solve for \( x \): \( x + 8 = 15 \).
5. Solve for \( x \): \( 4x = 20 \).
6. Solve the two-step equation: \( 3x + 7 = 22 \).
7. Solve for \( x \): \( \frac{x + 2}{3} = 5 \).
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### Part 3: Linear Graphs
8. What is the equation of a linear graph with a gradient of 2 and a y-intercept of -3?
9. Calculate the gradient of a line passing through points (1, 2) and (4, 6).
10. A linear graph passes through the points (0, 5) and (2, 9). Write the equation of the line.
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### Part 4: Geometry
11. What is the sum of the angles in a triangle?
12. Multiple Choice: Which of the following pairs of angles are equal in parallel lines cut by a transversal?
a) Corresponding angles
b) Co-interior angles
c) Alternate angles
d) Both a and c
13. A quadrilateral has angles measuring 90°, 85°, 95°, and an unknown angle. Find the unknown angle.
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### Part 5: Congruence and Similarity
14. Name the condition for congruence: Two triangles have two sides and the included angle equal.
15. If two triangles are similar and one side of the smaller triangle is 5 cm, corresponding to a side of 10 cm in the larger triangle, what is the ratio of their areas?
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### Part 6: Measurement
16. Find the area and perimeter of a rectangle with length 10 cm and width 7 cm.
17. Calculate the circumference of a circle with a radius of 3 cm. (Use \( \pi \approx 3.14 \)).
18. A parallelogram has a base of 8 cm and a height of 5 cm. Find its area.
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### Part 7: Problem-Solving
19. A word problem: A number is multiplied by 4, and then 7 is subtracted, resulting in 25. Find the number.
20. A linear graph intersects the y-axis at 4 and the x-axis at -2. Write the equation of the graph.