Daily Practice · Higher Plus
November 1965 5-a-day
Printing for a group?
The batch download puts all 5 tiers' November 1965 sheets in a single PDF, each tier behind its own divider page - 150 sheets in one file.
Every sheet in November 1965
The same date always regenerates the same five questions, so a sheet you print today is the sheet a classmate prints tomorrow.
- 1st November 1965A block has mass 830 g (to the nearest 10 g) and volume 12 cm^3 (to the nearest cm^3). Work out the upper bound of its density, to 2 decimal places.
- 2nd November 1965Work out the nth term of the quadratic sequence -1, -2, -1, 2, ...
- 3rd November 1965y is directly proportional to sqrt(x). When x = 9, y = 9. Work out y when x = 36.
- 4th November 1965A cuboid measures 11 cm by 7 cm by 14 cm tall. Work out the angle between its longest internal diagonal and the base, to 1 decimal place.
- 5th November 1965A bag holds 5 red, 6 blue and 5 green counters. Two are taken without replacement. Given neither is green, what is the probability both are red?
- 6th November 1965On a histogram, a 4-wide bar and a 16-wide bar have the same frequency density of 3. How many more values are in the wider class?
- 7th November 1965x = 195 and y = 114, each correct to the nearest whole number. Work out the upper bound of x - y.
- 8th November 1965The point (0, -5) lies on y = f(x). Write down its image on y = f(x) + 5.
- 9th November 1965A train slows steadily from 30 m/s to rest in 5 seconds. Work out its deceleration.
- 10th November 1965The point (9, 40) lies on the circle x^2 + y^2 = 1681. Work out the gradient of the tangent to the circle at that point.
- 11th November 1965A bag holds 6 counters, r of them red. Two are taken without replacement and P(both red) = 2/5. Work out r.
- 12th November 1965A histogram has two bars: one 20 units wide with frequency density 2.5, one 10 units wide with density 3. How many values in total?
- 13th November 1965A car covers 520 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.
- 14th November 1965Prove that the sum of 5 consecutive integers is always a multiple of 5. State the simplified sum you would use.
- 15th November 1965y is inversely proportional to x^2. When x = 5, y = 144. Work out y when x = 6.
- 16th November 1965In a circle theorem proof, a step uses the fact that OA and OB are both radii of the circle, so triangle OAB is isosceles. State the reason being quoted.
- 17th November 1965The probability of winning a game is 3/8. A player expects 30 wins. How many games did they play?
- 18th November 1965On a histogram, a 5-wide bar and a 10-wide bar have the same frequency density of 2.5. How many more values are in the wider class?
- 19th November 1965Rationalise the denominator of 88/sqrt(11), giving your answer in its simplest form.
- 20th November 1965f(x) = 3x - 1 and g(x) = 3x - 6. Work out fg(5).
- 21st November 1965y is directly proportional to x^3. When x = 4, y = 320. Work out y when x = 2.
- 22nd November 1965In a vector proof you find that vector PQ = a - 6b and vector RS = 2a - 12b. What does this show about PQ and RS?
- 23rd November 1965A bag holds 7 red and n blue counters. The probability of taking a red is 7/9. Work out n.
- 24th November 1965A histogram has two bars: one 20 units wide with frequency density 2, one 5 units wide with density 3.5. How many values in total?
- 25th November 1965Simplify sqrt(72) + sqrt(72), giving your answer in the form a sqrt(b).
- 26th November 1965The curve y = sin x° is drawn for 0 <= x <= 360. Write down the value of y when x = 180.
- 27th November 1965y is directly proportional to sqrt(x). When x = 36, y = 12. Work out y when x = 4.
- 28th November 1965A cuboid measures 10 cm by 15 cm by 13 cm. Work out the length of the longest diagonal inside it, to 1 decimal place.
- 29th November 1965A bag holds 3 red and 9 blue counters. Two are taken without replacement. Given the first was red, what is the probability the second is blue?
- 30th November 1965On a histogram, a 10-wide bar and a 20-wide bar have the same frequency density of 1.5. How many more values are in the wider class?