Daily Practice · Higher Plus
April 1964 5-a-day
Printing for a group?
The batch download puts all 5 tiers' April 1964 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in April 1964
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st April 1964In a vector proof you find that vector PQ = 5a + 5b and vector RS = 10a + 10b. What does this show about PQ and RS?
- 2nd April 1964A bag holds 5 red and n blue counters. The probability of taking a red is 5/7. Work out n.
- 3rd April 1964A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 0.8. How many values in total?
- 4th April 1964A car covers 670 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.
- 5th April 1964Solve x^2 + 2x > 0.
- 6th April 1964y is directly proportional to sqrt(x). When x = 49, y = 63. Work out y when x = 25.
- 7th April 1964A cuboid measures 6 cm by 7 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 8th April 1964A bag holds 3 red and 7 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 9th April 1964On 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 1964Rationalise the denominator of 18/sqrt(2), giving your answer in its simplest form.
- 11th April 1964Write x^2 - 10x - 2 in the form (x + a)^2 + b.
- 12th April 1964A train slows steadily from 21 m/s to rest in 10 seconds. Work out its deceleration.
- 13th April 1964A cuboid measures 5 cm by 8 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 14th April 1964A bag holds 7 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 15th April 1964A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 1.4. How many values in total?
- 16th April 1964Simplify sqrt(48) + sqrt(12), giving your answer in the form a sqrt(b).
- 17th April 1964Work out the coordinates of the turning point of y = x^2 - 16x + 3.
- 18th April 1964y is inversely proportional to x^2. When x = 5, y = 9. Work out y when x = 3.
- 19th April 1964The 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.
- 20th April 1964A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 1/55. Work out r.
- 21st April 1964On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 22nd April 1964A rectangle is 4 cm by 25 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 23rd April 1964Simplify (x^2 - 2x - 3)/(x - 3).
- 24th April 1964y is directly proportional to x^3. When x = 2, y = 16. Work out y when x = 5.
- 25th April 1964In a circle theorem proof, a step uses the fact that the angle in a semicircle is being proved. State the reason being quoted.
- 26th April 1964The probability of winning a game is 3/5. A player expects 18 wins. How many games did they play?
- 27th April 1964A 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?
- 28th April 1964Expand and simplify (6 + sqrt(11))(6 - sqrt(11)).
- 29th April 1964In an algebraic proof, how would you write three consecutive even numbers in terms of an integer n?
- 30th April 1964y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 4.