Daily Practice · Higher Plus
July 1968 5-a-day
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The batch download puts all 5 tiers' July 1968 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1968
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1968Simplify (x^2 + 3x - 4)/(x + 4).
- 2nd July 1968y is inversely proportional to x^2. When x = 2, y = 16. Work out y when x = 4.
- 3rd July 1968In a circle theorem proof, a step uses the fact that a radius is drawn to the midpoint of a chord. State the reason being quoted.
- 4th July 1968The probability of winning a game is 1/5. A player expects 14 wins. How many games did they play?
- 5th July 1968On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 6th July 1968A car covers 590 m (to the nearest 10 m) in 8 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th July 1968In an algebraic proof, how would you write the product of two consecutive integers in terms of an integer n?
- 8th July 1968y is directly proportional to x^3. When x = 4, y = 256. Work out y when x = 3.
- 9th July 1968In a vector proof you find that vector PQ = 5a + 3b and vector RS = 20a + 12b. What does this show about PQ and RS?
- 10th July 1968A bag holds 7 red and n blue counters. The probability of taking a red is 1/2. Work out n.
- 11th July 1968A histogram has two bars: one 20 units wide with frequency density 0.4, one 5 units wide with density 3.5. How many values in total?
- 12th July 1968Rationalise the denominator of 18/sqrt(3), giving your answer in its simplest form.
- 13th July 1968Make x the subject of 8x + 7 = y(x + 7).
- 14th July 1968y is directly proportional to sqrt(x). When x = 36, y = 36. Work out y when x = 49.
- 15th July 1968A cuboid measures 15 cm by 6 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 16th July 1968A bag holds 6 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 17th July 1968On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 18th July 1968Simplify sqrt(32) + sqrt(2), giving your answer in the form a sqrt(b).
- 19th July 1968Write 6/(x - 4) + 5/(x + 4) as a single fraction.
- 20th July 1968A train slows steadily from 27 m/s to rest in 5 seconds. Work out its deceleration.
- 21st July 1968A cuboid measures 11 cm by 10 cm by 5 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 22nd July 1968A bag holds 5 red, 3 blue and 2 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 23rd July 1968A histogram has two bars: one 20 units wide with frequency density 2.5, one 5 units wide with density 3. How many values in total?
- 24th July 1968A rectangle is 6 cm by 13 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th July 1968Solve 6x^2 + 17x + 12 = 0.
- 26th July 1968y is inversely proportional to x^2. When x = 3, y = 75. Work out y when x = 5.
- 27th July 1968The 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.
- 28th July 1968A bag holds 11 counters, r of them red. Two are taken without replacement and P(both red) = 21/55. Work out r.
- 29th July 1968On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th July 1968Expand and simplify (5 + sqrt(6))(5 - sqrt(6)).
- 31st July 1968f(x) = 7x + 3. Work out the inverse function f^-1(x).