Daily Practice · Higher Plus
April 1954 5-a-day
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The batch download puts all 5 tiers' April 1954 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1954
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1954A bag holds 6 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 2nd April 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 3rd April 1954A car covers 690 m (to the nearest 10 m) in 5 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 4th April 1954Simplify (x^2 + 7x + 12)/(x + 4).
- 5th April 1954y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 2.
- 6th April 1954A cuboid measures 10 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 7th April 1954A bag holds 3 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 8th April 1954A histogram has two bars: one 10 units wide with frequency density 1.2, one 20 units wide with density 3.5. How many values in total?
- 9th April 1954Rationalise the denominator of 60/sqrt(5), giving your answer in its simplest form.
- 10th April 1954In an algebraic proof, how would you write three consecutive integers in terms of an integer n?
- 11th April 1954y is directly proportional to sqrt(x). When x = 25, y = 40. Work out y when x = 49.
- 12th April 1954The point (3, 4) lies on the circle x^2 + y^2 = 25. Work out the gradient of the tangent to the circle at that point.
- 13th April 1954A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 14th April 1954On a histogram, a 4-wide bar and a 8-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 15th April 1954Simplify sqrt(8) + sqrt(98), giving your answer in the form a sqrt(b).
- 16th April 1954Make x the subject of 4x + 4 = y(x + 4).
- 17th April 1954A train slows steadily from 27 m/s to rest in 8 seconds. Work out its deceleration.
- 18th April 1954In a circle theorem proof, a step uses the fact that a tangent meets a radius at the point of contact. State the reason being quoted.
- 19th April 1954The probability of winning a game is 1/2. A player expects 24 wins. How many games did they play?
- 20th April 1954A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 21st April 1954A rectangle is 17 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 22nd April 1954Write 7/(x + 1) + 2/(x + 4) as a single fraction.
- 23rd April 1954y is inversely proportional to x^2. When x = 2, y = 100. Work out y when x = 5.
- 24th April 1954In a vector proof you find that vector PQ = 4a + 4b and vector RS = 16a + 16b. What does this show about PQ and RS?
- 25th April 1954A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 26th April 1954On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 27th April 1954Expand and simplify (5 + sqrt(11))(5 - sqrt(11)).
- 28th April 1954Solve 6x^2 + x - 2 = 0.
- 29th April 1954y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 2.
- 30th April 1954A cuboid measures 6 cm by 15 cm by 9 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.