Daily Practice · Higher Plus
July 1963 5-a-day
Printing for a group?
The batch download puts all 5 tiers' July 1963 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1963
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1963The probability of winning a game is 1/2. A player expects 25 wins. How many games did they play?
- 2nd July 1963A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 1.4. How many values in total?
- 3rd July 1963A rectangle is 18 cm by 10 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 4th July 1963Make x the subject of 4x + 2 = y(x + 2).
- 5th July 1963y is inversely proportional to x^2. When x = 4, y = 36. Work out y when x = 6.
- 6th July 1963In a vector proof you find that vector PQ = 3a - 4b and vector RS = 9a - 12b. What does this show about PQ and RS?
- 7th July 1963A bag holds 5 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 8th July 1963On 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?
- 9th July 1963Expand and simplify (2 + sqrt(2))(2 - sqrt(2)).
- 10th July 1963Write 6/(x + 3) + 7/(x + 1) as a single fraction.
- 11th July 1963y is directly proportional to x^3. When x = 2, y = 24. Work out y when x = 5.
- 12th July 1963A cuboid measures 10 cm by 11 cm by 12 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 13th July 1963A 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?
- 14th July 1963A histogram has two bars: one 20 units wide with frequency density 0.4, one 20 units wide with density 3.5. How many values in total?
- 15th July 1963A block has mass 500 g (to the nearest 10 g) and volume 19 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 16th July 1963Solve 12x^2 - 7x + 1 = 0.
- 17th July 1963y is directly proportional to sqrt(x). When x = 16, y = 8. Work out y when x = 64.
- 18th July 1963A cuboid measures 5 cm by 12 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 19th July 1963A bag holds 6 red, 7 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 20th July 1963On a histogram, a 10-wide bar and a 30-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 21st July 1963x = 176 and y = 163, each correct to the nearest whole number. Work out the upper bound of x - y.
- 22nd July 1963f(x) = 5x - 9. Work out the inverse function f^-1(x).
- 23rd July 1963A train slows steadily from 16 m/s to rest in 4 seconds. Work out its deceleration.
- 24th July 1963The point (12, 16) lies on the circle x^2 + y^2 = 400. Work out the gradient of the tangent to the circle at that point.
- 25th July 1963A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 26th July 1963A histogram has two bars: one 5 units wide with frequency density 1.5, one 25 units wide with density 3. How many values in total?
- 27th July 1963A car covers 590 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.
- 28th July 1963Solve x^2 + y^2 = 225 and y = x + 3 simultaneously.
- 29th July 1963y is inversely proportional to x^2. When x = 5, y = 72. Work out y when x = 6.
- 30th July 1963In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 31st July 1963The probability of winning a game is 1/5. A player expects 5 wins. How many games did they play?