Daily Practice · Higher Plus
April 1957 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1957 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1957
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1957A train slows steadily from 34 m/s to rest in 10 seconds. Work out its deceleration.
- 2nd April 1957In 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.
- 3rd April 1957The probability of winning a game is 4/5. A player expects 104 wins. How many games did they play?
- 4th April 1957A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 5th April 1957Rationalise the denominator of 60/sqrt(6), giving your answer in its simplest form.
- 6th April 1957A quadratic sequence starts 5, 13, 23, 35. Work out the second difference, and the coefficient of n^2.
- 7th April 1957y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 8th April 1957In a vector proof you find that vector PQ = 3a + 5b and vector RS = 15a + 25b. What does this show about PQ and RS?
- 9th April 1957A bag holds 5 red and n blue counters. The probability of taking a red is 5/8. Work out n.
- 10th April 1957On 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?
- 11th April 1957Simplify sqrt(20) + sqrt(5), giving your answer in the form a sqrt(b).
- 12th April 1957Solve x^2 + 3x > 0.
- 13th April 1957y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 14th April 1957A cuboid measures 6 cm by 6 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 15th April 1957A bag holds 3 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 16th April 1957A histogram has two bars: one 20 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 17th April 1957A rectangle is 13 cm by 5 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 18th April 1957Write x^2 + 14x - 13 in the form (x + a)^2 + b.
- 19th April 1957y is directly proportional to sqrt(x). When x = 36, y = 30. Work out y when x = 25.
- 20th April 1957A cuboid measures 12 cm by 11 cm by 9 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 21st April 1957A bag holds 7 red, 6 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 22nd April 1957On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 23rd April 1957Expand and simplify (4 + sqrt(7))(4 - sqrt(7)).
- 24th April 1957Work out the coordinates of the turning point of y = x^2 - 2x + 9.
- 25th April 1957A train slows steadily from 24 m/s to rest in 5 seconds. Work out its deceleration.
- 26th April 1957The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 27th April 1957A bag holds 8 counters, r of them red. Two are taken without replacement and P(both red) = 3/14. Work out r.
- 28th April 1957A histogram has two bars: one 5 units wide with frequency density 2, one 10 units wide with density 3. How many values in total?
- 29th April 1957A block has mass 270 g (to the nearest 10 g) and volume 7 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 30th April 1957Simplify (x^2 + 2x - 48)/(x - 6).