Daily Practice · Higher Plus
August 1977 5-a-day
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The batch download puts all 5 tiers' August 1977 sheets in a single PDF, each tier behind its own divider page - 155 sheets in one file.
Every sheet in August 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st August 1977The point (-4, 0) lies on y = f(x). Write down its image on y = f(x) - 4.
- 2nd August 1977y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 3rd August 1977A cuboid measures 13 cm by 13 cm by 13 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 4th August 1977A bag holds 5 red, 5 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 5th August 1977A histogram has two bars: one 10 units wide with frequency density 0.4, one 10 units wide with density 0.6. How many values in total?
- 6th August 1977A car covers 430 m (to the nearest 10 m) in 2 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 7th August 1977Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 8th August 1977y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 36.
- 9th August 1977The 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.
- 10th August 1977A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 1/5. Work out r.
- 11th August 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?
- 12th August 1977Rationalise the denominator of 42/sqrt(7), giving your answer in its simplest form.
- 13th August 1977f(x) = 4x - 3 and g(x) = 5x - 3. Work out fg(3).
- 14th August 1977A train slows steadily from 33 m/s to rest in 5 seconds. Work out its deceleration.
- 15th August 1977In a circle theorem proof, a step uses the fact that opposite angles of a cyclic quadrilateral are being proved. State the reason being quoted.
- 16th August 1977The probability of winning a game is 3/5. A player expects 39 wins. How many games did they play?
- 17th August 1977A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 0.8. How many values in total?
- 18th August 1977Simplify sqrt(8) + sqrt(18), giving your answer in the form a sqrt(b).
- 19th August 1977The curve y = cos x° is drawn for 0 <= x <= 360. Write down the value of y when x = 270.
- 20th August 1977y is inversely proportional to x^2. When x = 3, y = 16. Work out y when x = 4.
- 21st August 1977In a vector proof you find that vector PQ = 4a - b and vector RS = 8a - 2b. What does this show about PQ and RS?
- 22nd August 1977A bag holds 3 red and n blue counters. The probability of taking a red is 3/10. Work out n.
- 23rd August 1977On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 24th August 1977A rectangle is 27 cm by 16 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 25th August 1977A quadratic sequence starts 0, 8, 24, 48. Work out the second difference, and the coefficient of n^2.
- 26th August 1977y is directly proportional to x^3. When x = 3, y = 81. Work out y when x = 4.
- 27th August 1977A cuboid measures 3 cm by 3 cm by 3 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 28th August 1977A bag holds 5 red and 5 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 29th August 1977A histogram has two bars: one 5 units wide with frequency density 1.2, one 5 units wide with density 3.5. How many values in total?
- 30th August 1977Expand and simplify (9 + sqrt(11))(9 - sqrt(11)).
- 31st August 1977Solve x^2 - 12x + 20 < 0.