Daily Practice · Higher Plus
April 1972 5-a-day
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The batch download puts all 5 tiers' April 1972 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1972
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1972A cuboid measures 8 cm by 11 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd April 1972A bag holds 4 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd April 1972On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 4th April 1972Expand and simplify (5 + sqrt(5))(5 - sqrt(5)).
- 5th April 1972Work out the nth term of the quadratic sequence 4, 9, 18, 31, ...
- 6th April 1972y is directly proportional to x^3. When x = 3, y = 108. Work out y when x = 4.
- 7th April 1972The point (7, 24) lies on the circle x^2 + y^2 = 625. Work out the gradient of the tangent to the circle at that point.
- 8th April 1972A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/11. Work out r.
- 9th April 1972A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 0.6. How many values in total?
- 10th April 1972A block has mass 450 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 11th April 1972The point (3, 2) lies on y = f(x). Write down its image on y = f(-x).
- 12th April 1972y is directly proportional to sqrt(x). When x = 36, y = 24. Work out y when x = 25.
- 13th April 1972In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 14th April 1972The probability of winning a game is 1/2. A player expects 15 wins. How many games did they play?
- 15th April 1972On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 16th April 1972x = 77 and y = 56, each correct to the nearest whole number. Work out the upper bound of x - y.
- 17th April 1972Prove that the sum of 7 consecutive integers is always a multiple of 7. State the simplified sum you would use.
- 18th April 1972A train slows steadily from 16 m/s to rest in 5 seconds. Work out its deceleration.
- 19th April 1972In a vector proof you find that vector PQ = 4a + b and vector RS = 8a + 2b. What does this show about PQ and RS?
- 20th April 1972A bag holds 3 red and n blue counters. The probability of taking a red is 1/3. Work out n.
- 21st April 1972A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3. How many values in total?
- 22nd April 1972A car covers 800 m (to the nearest 10 m) in 9 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 23rd April 1972f(x) = 4x - 1 and g(x) = 4x + 8. Work out fg(6).
- 24th April 1972y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 25th April 1972A cuboid measures 12 cm by 4 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th April 1972A bag holds 7 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th April 1972On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 28th April 1972Rationalise the denominator of 27/sqrt(3), giving your answer in its simplest form.
- 29th April 1972The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 30th April 1972y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 2.