Mathematics Foundation and Higher Flashcards

A shop reduces the price of a jacket from £80 to £60. What is the percentage decrease?

Answer: 25%

The decrease is £80 - £60 = £20. Percentage decrease = (20 ÷ 80) × 100 = 25%. Always divide the change by the original value, not the new value.

Simplify the expression 3x + 5y - 2x + 4y.

Answer: x + 9y

Collect like terms: 3x - 2x = x, and 5y + 4y = 9y. So the simplified expression is x + 9y.

What is the area of a triangle with a base of 12 cm and a height of 8 cm?

Answer: 48 cm²

The area of a triangle is ½ × base × height = ½ × 12 × 8 = 48 cm². This formula works because a triangle is exactly half of a rectangle with the same base and height.

Solve the equation 4x - 7 = 13.

Answer: x = 5

Add 7 to both sides: 4x = 20. Then divide both sides by 4: x = 5. You can check by substituting back: 4(5) - 7 = 20 - 7 = 13 ✓

A bag contains 3 red, 5 blue, and 2 green marbles. What is the probability of randomly selecting a blue marble?

Answer: 1/2

Total marbles = 3 + 5 + 2 = 10. Probability of blue = 5/10 = 1/2. Probability is always favourable outcomes divided by total outcomes.

What is the value of 2³ × 2⁴?

Answer: 2⁷

When multiplying powers with the same base, add the indices: 2³ × 2⁴ = 2^(3+4) = 2⁷ = 128. This is one of the fundamental index laws.