Daily Practice · Higher Plus
September 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' September 1965 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in September 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st September 1965A 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?
- 2nd September 1965Simplify sqrt(32) + sqrt(50), giving your answer in the form a sqrt(b).
- 3rd September 1965Write x^2 + 10x - 14 in the form (x + a)^2 + b.
- 4th September 1965y is inversely proportional to x^2. When x = 2, y = 9. Work out y when x = 3.
- 5th September 1965A cuboid measures 4 cm by 8 cm by 12 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 6th September 1965A bag holds 4 red, 3 blue and 4 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 7th September 1965On a histogram, a 5-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?
- 8th September 1965A rectangle is 29 cm by 19 cm, each correct to the nearest cm. Work out the upper bound of its area.
- 9th September 1965Work out the coordinates of the turning point of y = x^2 - 8x - 4.
- 10th September 1965y is directly proportional to x^3. When x = 2, y = 48. Work out y when x = 5.
- 11th September 1965The 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.
- 12th September 1965A bag holds 7 counters, r of them red. Two are taken without replacement and P(both red) = 10/21. Work out r.
- 13th September 1965A histogram has two bars: one 10 units wide with frequency density 1.5, one 5 units wide with density 0.6. How many values in total?
- 14th September 1965Expand and simplify (6 + sqrt(2))(6 - sqrt(2)).
- 15th September 1965Simplify (x^2 + 4x - 12)/(x + 6).
- 16th September 1965y is directly proportional to sqrt(x). When x = 9, y = 15. Work out y when x = 36.
- 17th September 1965In a circle theorem proof, a step uses the fact that the three angles of triangle OAB are being summed. State the reason being quoted.
- 18th September 1965The probability of winning a game is 3/5. A player expects 9 wins. How many games did they play?
- 19th September 1965On 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?
- 20th September 1965A block has mass 250 g (to the nearest 10 g) and volume 10 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 21st September 1965In an algebraic proof, how would you write a multiple of 9 in terms of an integer n?
- 22nd September 1965A train slows steadily from 37 m/s to rest in 5 seconds. Work out its deceleration.
- 23rd September 1965In a vector proof you find that vector PQ = 3a - 6b and vector RS = 15a - 30b. What does this show about PQ and RS?
- 24th September 1965A bag holds 4 red and n blue counters. The probability of taking a red is 2/3. Work out n.
- 25th September 1965A histogram has two bars: one 20 units wide with frequency density 2.5, one 25 units wide with density 0.6. How many values in total?
- 26th September 1965x = 178 and y = 56, each correct to the nearest whole number. Work out the upper bound of x - y.
- 27th September 1965Make x the subject of 7x + 2 = y(x + 2).
- 28th September 1965y is inversely proportional to x^2. When x = 5, y = 32. Work out y when x = 4.
- 29th September 1965A cuboid measures 3 cm by 5 cm by 10 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 30th September 1965A bag holds 4 red and 6 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?