Daily Practice · Higher Plus
July 1975 5-a-day
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The batch download puts all 5 tiers' July 1975 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1975
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1975In an algebraic proof, how would you write two consecutive odd numbers in terms of an integer n?
- 2nd July 1975y is directly proportional to sqrt(x). When x = 16, y = 28. Work out y when x = 81.
- 3rd July 1975In a vector proof you find that vector PQ = a + 6b and vector RS = 3a + 18b. What does this show about PQ and RS?
- 4th July 1975A bag holds 8 red and n blue counters. The probability of taking a red is 8/13. Work out n.
- 5th July 1975On 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?
- 6th July 1975x = 53 and y = 8, each correct to the nearest whole number. Work out the upper bound of x - y.
- 7th July 1975Make x the subject of 7x + 3 = y(x + 3).
- 8th July 1975A train slows steadily from 40 m/s to rest in 4 seconds. Work out its deceleration.
- 9th July 1975A cuboid measures 10 cm by 9 cm by 6 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 10th July 1975A bag holds 5 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 11th July 1975A histogram has two bars: one 10 units wide with frequency density 2, one 20 units wide with density 3. How many values in total?
- 12th July 1975A car covers 400 m (to the nearest 10 m) in 6 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 13th July 1975Write 5/(x - 1) + 7/(x - 6) as a single fraction.
- 14th July 1975y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 15th July 1975A cuboid measures 5 cm by 4 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 16th July 1975A bag holds 7 red, 7 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 17th July 1975On 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?
- 18th July 1975Rationalise the denominator of 36/sqrt(3), giving your answer in its simplest form.
- 19th July 1975Solve 3x^2 - 7x - 6 = 0.
- 20th July 1975y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 5.
- 21st July 1975The point (5, 12) lies on the circle x^2 + y^2 = 169. Work out the gradient of the tangent to the circle at that point.
- 22nd July 1975A bag holds 12 counters, r of them red. Two are taken without replacement and P(both red) = 14/33. Work out r.
- 23rd July 1975A histogram has two bars: one 10 units wide with frequency density 1.2, one 25 units wide with density 3. How many values in total?
- 24th July 1975Simplify sqrt(18) + sqrt(72), giving your answer in the form a sqrt(b).
- 25th July 1975f(x) = 7x + 8. Work out the inverse function f^-1(x).
- 26th July 1975y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 81.
- 27th July 1975In a circle theorem proof, a step uses the fact that two tangents are drawn to a circle from the same external point. State the reason being quoted.
- 28th July 1975The probability of winning a game is 3/4. A player expects 9 wins. How many games did they play?
- 29th July 1975On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 30th July 1975A rectangle is 10 cm by 8 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 31st July 1975Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.