Daily Practice · Higher Plus
April 1953 5-a-day
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The batch download puts all 5 tiers' April 1953 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1953
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1953A histogram has two bars: one 20 units wide with frequency density 2, one 25 units wide with density 0.8. How many values in total?
- 2nd April 1953Simplify sqrt(18) + sqrt(2), giving your answer in the form a sqrt(b).
- 3rd April 1953Use the iteration x(n+1) = cube root of (8x(n) + 8) with x(0) = 5. Work out x(1) to 3 decimal places.
- 4th April 1953y is inversely proportional to x^2. When x = 4, y = 50. Work out y when x = 5.
- 5th April 1953A cuboid measures 5 cm by 3 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 6th April 1953A 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?
- 7th April 1953On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th April 1953A rectangle is 12 cm by 24 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th April 1953Work out the nth term of the quadratic sequence 0, 2, 6, 12, ...
- 10th April 1953y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 11th April 1953A cuboid measures 8 cm by 14 cm by 6 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 12th April 1953A bag holds 4 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 13th April 1953A histogram has two bars: one 10 units wide with frequency density 2, one 5 units wide with density 1.4. How many values in total?
- 14th April 1953Expand and simplify (7 + sqrt(11))(7 - sqrt(11)).
- 15th April 1953The point (3, 3) lies on y = f(x). Write down its image on y = -f(x).
- 16th April 1953y is directly proportional to sqrt(x). When x = 49, y = 56. Work out y when x = 9.
- 17th April 1953The 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.
- 18th April 1953A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 1/66. Work out r.
- 19th April 1953On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 20th April 1953A block has mass 640 g (to the nearest 10 g) and volume 21 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st April 1953Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 22nd April 1953A train slows steadily from 12 m/s to rest in 10 seconds. Work out its deceleration.
- 23rd April 1953In a circle theorem proof, a step uses the fact that two angles at the circumference stand on the same arc. State the reason being quoted.
- 24th April 1953The probability of winning a game is 2/5. A player expects 10 wins. How many games did they play?
- 25th April 1953A histogram has two bars: one 10 units wide with frequency density 1.2, one 10 units wide with density 3.5. How many values in total?
- 26th April 1953x = 49 and y = 14, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th April 1953f(x) = 2x + 3 and g(x) = 4x - 4. Work out fg(5).
- 28th April 1953y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 29th April 1953In a vector proof you find that vector PQ = 6a + 4b and vector RS = 12a + 8b. What does this show about PQ and RS?
- 30th April 1953A bag holds 8 red and n blue counters. The probability of taking a red is 4/7. Work out n.