Daily Practice · Higher Plus
April 1955 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1955 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1955
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1955A cuboid measures 12 cm by 10 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 2nd April 1955A bag holds 5 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 3rd April 1955A histogram has two bars: one 5 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 4th April 1955A block has mass 560 g (to the nearest 10 g) and volume 24 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 5th April 1955Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 6th April 1955y is directly proportional to sqrt(x). When x = 36, y = 42. Work out y when x = 16.
- 7th April 1955The point (10, 24) lies on the circle x^2 + y^2 = 676. Work out the gradient of the tangent to the circle at that point.
- 8th April 1955A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 9th April 1955On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 10th April 1955x = 179 and y = 150, each correct to the nearest whole number. Work out the upper bound of x - y.
- 11th April 1955f(x) = 6x + 7 and g(x) = 6x + 9. Work out fg(4).
- 12th April 1955A train slows steadily from 29 m/s to rest in 5 seconds. Work out its deceleration.
- 13th April 1955In 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.
- 14th April 1955The probability of winning a game is 2/5. A player expects 48 wins. How many games did they play?
- 15th April 1955A histogram has two bars: one 20 units wide with frequency density 1.5, one 5 units wide with density 3. How many values in total?
- 16th April 1955A car covers 900 m (to the nearest 10 m) in 4 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 17th April 1955The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 360.
- 18th April 1955y is inversely proportional to x^2. When x = 2, y = 36. Work out y when x = 3.
- 19th April 1955In a vector proof you find that vector PQ = 5a - 4b and vector RS = 10a - 8b. What does this show about PQ and RS?
- 20th April 1955A bag holds 7 red and n blue counters. The probability of taking a red is 7/15. Work out n.
- 21st April 1955On 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?
- 22nd April 1955Rationalise the denominator of 22/sqrt(2), giving your answer in its simplest form.
- 23rd April 1955A quadratic sequence starts -1, 12, 35, 68. Work out the second difference, and the coefficient of n^2.
- 24th April 1955y is directly proportional to x^3. When x = 3, y = 162. Work out y when x = 5.
- 25th April 1955A cuboid measures 15 cm by 4 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 26th April 1955A bag holds 4 red and 4 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 27th April 1955A histogram has two bars: one 5 units wide with frequency density 1.5, one 20 units wide with density 0.6. How many values in total?
- 28th April 1955Simplify sqrt(80) + sqrt(245), giving your answer in the form a sqrt(b).
- 29th April 1955Solve x^2 - 7x < 0.
- 30th April 1955y is directly proportional to sqrt(x). When x = 16, y = 32. Work out y when x = 64.