Daily Practice · Higher Plus
July 1977 5-a-day
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The batch download puts all 5 tiers' July 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in July 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st July 1977Rationalise the denominator of 30/sqrt(5), giving your answer in its simplest form.
- 2nd July 1977Solve 8x^2 + 10x + 3 = 0.
- 3rd July 1977y is inversely proportional to x^2. When x = 4, y = 12. Work out y when x = 2.
- 4th July 1977A cuboid measures 8 cm by 7 cm by 11 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th July 1977A bag holds 6 red, 5 blue and 6 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th July 1977On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 7th July 1977Simplify sqrt(75) + sqrt(27), giving your answer in the form a sqrt(b).
- 8th July 1977f(x) = 2x - 8. Work out the inverse function f^-1(x).
- 9th July 1977y is directly proportional to x^3. When x = 2, y = 40. Work out y when x = 4.
- 10th July 1977The point (20, 21) lies on the circle x^2 + y^2 = 841. Work out the gradient of the tangent to the circle at that point.
- 11th July 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 3/10. Work out r.
- 12th July 1977A histogram has two bars: one 10 units wide with frequency density 0.4, one 20 units wide with density 0.6. How many values in total?
- 13th July 1977A rectangle is 17 cm by 21 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 14th July 1977Solve x^2 + y^2 = 225 and y = x - 3 simultaneously.
- 15th July 1977y is directly proportional to sqrt(x). When x = 36, y = 48. Work out y when x = 9.
- 16th July 1977In a circle theorem proof, a step uses the fact that a triangle is drawn from the ends of a diameter to a point on the circle. State the reason being quoted.
- 17th July 1977The probability of winning a game is 1/8. A player expects 3 wins. How many games did they play?
- 18th July 1977On a histogram, a 4-wide bar and a 12-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th July 1977Expand and simplify (4 + sqrt(2))(4 - sqrt(2)).
- 20th July 1977Use the iteration x(n+1) = cube root of (9x(n) + 5) with x(0) = 5. Work out x(1) to 3 decimal places.
- 21st July 1977A train slows steadily from 33 m/s to rest in 10 seconds. Work out its deceleration.
- 22nd July 1977In a vector proof you find that vector PQ = 4a - b and vector RS = 20a - 5b. What does this show about PQ and RS?
- 23rd July 1977A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 24th July 1977A histogram has two bars: one 5 units wide with frequency density 2.5, one 5 units wide with density 3.5. How many values in total?
- 25th July 1977A block has mass 640 g (to the nearest 10 g) and volume 9 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 26th July 1977Work out the nth term of the quadratic sequence 8, 17, 34, 59, ...
- 27th July 1977y is inversely proportional to x^2. When x = 3, y = 8. Work out y when x = 2.
- 28th July 1977A cuboid measures 6 cm by 3 cm by 4 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th July 1977A bag holds 11 red and 3 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th July 1977On a histogram, a 5-wide bar and a 15-wide bar have the same frequency density of 2. How many more values are in the wider class?
- 31st July 1977x = 130 and y = 20, each correct to the nearest whole number. Work out the upper bound of x - y.