Daily Practice · Higher Plus
September 1977 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1977 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1977
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1977y is directly proportional to sqrt(x). When x = 16, y = 12. Work out y when x = 36.
- 2nd September 1977A cuboid measures 12 cm by 7 cm by 10 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 3rd September 1977A bag holds 6 red, 4 blue and 3 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 4th September 1977On 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?
- 5th September 1977A block has mass 350 g (to the nearest 10 g) and volume 20 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 6th September 1977Write x^2 + 16x + 4 in the form (x + a)^2 + b.
- 7th September 1977A train slows steadily from 39 m/s to rest in 8 seconds. Work out its deceleration.
- 8th September 1977The point (9, 12) lies on the circle x^2 + y^2 = 225. Work out the gradient of the tangent to the circle at that point.
- 9th September 1977A bag holds 5 counters, r of them red. Two are taken without replacement and P(both red) = 1/10. Work out r.
- 10th September 1977A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 0.6. How many values in total?
- 11th September 1977x = 75 and y = 28, each correct to the nearest whole number. Work out the upper bound of x - y.
- 12th September 1977Work out the coordinates of the turning point of y = x^2 - 2x - 4.
- 13th September 1977y is inversely proportional to x^2. When x = 3, y = 12. Work out y when x = 2.
- 14th September 1977In 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.
- 15th September 1977The probability of winning a game is 1/4. A player expects 5 wins. How many games did they play?
- 16th September 1977On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 17th September 1977A car covers 290 m (to the nearest 10 m) in 3 s (to the nearest second). Work out the lower bound of its speed, to 2 decimal places.
- 18th September 1977Simplify (x^2 + 11x + 28)/(x + 7).
- 19th September 1977y is directly proportional to x^3. When x = 4, y = 192. Work out y when x = 3.
- 20th September 1977In a vector proof you find that vector PQ = 5a + 3b and vector RS = 25a + 15b. What does this show about PQ and RS?
- 21st September 1977A bag holds 8 red and n blue counters. The probability of taking a red is 8/15. Work out n.
- 22nd September 1977A histogram has two bars: one 5 units wide with frequency density 0.4, one 10 units wide with density 3.5. How many values in total?
- 23rd September 1977Rationalise the denominator of 48/sqrt(6), giving your answer in its simplest form.
- 24th September 1977In an algebraic proof, how would you write the next even number after 2n in terms of an integer n?
- 25th September 1977y is directly proportional to sqrt(x). When x = 9, y = 6. Work out y when x = 81.
- 26th September 1977A cuboid measures 6 cm by 10 cm by 15 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 27th September 1977A 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?
- 28th September 1977On a histogram, a 10-wide bar and a 40-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 29th September 1977Simplify sqrt(12) + sqrt(147), giving your answer in the form a sqrt(b).
- 30th September 1977Make x the subject of 7x + 6 = y(x + 6).